Someone gives you two dice. They offer to pay you €37 if you roll two 6s. However, it will cost you €1 a roll. What is the EV of this wager?
Double sixes = $1/36 = 0.028$
Other rolls = $35/36 = 0.972$
Do we calculate expectation value like this
0.028(€36) + 0.972(-€1) = x
or like this
0.028(€37) + 0.972(-€1) = x
I think we multiply postive outcomes(0.028) by money we will get €37 and substract bad outcomes (0.972) multiplied by €1 that we are loosing. But some say first equation is correct(€36). Are they right and why?